### Problem Statement: A sealed \(86 \, \text{m}^3\) tank is filled with 2000 moles of ideal oxygen gas (diatomic) at an initial temperature of 270 K. The gas is heated to a final temperature of 430 K. The atomic mass of oxygen is \(16.0 \, \text{g/mol}\). The mass density of the oxygen gas, in SI units, is closest to: - \(0.74\) - \(0.56\) - \(0.93\) - \(1.5\) - \(0.37\) ### Answer Choices: - \(0.74\) - \(0.56\) - \(0.93\) - \(1.5\) - \(0.37\) ### Instructions: Click Save and Submit to save and submit. Click Save All Answers to save all answers. --- ### Explanation of Key Concepts: 1. **Ideal Gas Law** - The relationship between pressure (P), volume (V), temperature (T), and number of moles (n) of an ideal gas is given by the equation: \[ PV = nRT \] Where \(R\) is the universal gas constant (\(8.314 \, \text{J/(mol·K)}\)). 2. **Density Calculation** - To find the mass density (\(\rho\)) of the gas, we need to calculate the mass (m) of the gas and then divide it by the volume (V): \[ \rho = \frac{m}{V} \] #### Steps to Calculate Density: 1. **Calculate the Molar Mass**: - The oxygen gas is diatomic, so the molar mass \(M(O_2)\) is \(32.0 \, \text{g/mol}\) (since \(16.0 \, \text{g/mol} \times 2\)). 2. **Calculate the Mass of the Gas**: - Use the number of moles and the molar mass to find the total mass: \[ m = n \times M(O_2) = 2000 \, \text{mol} \times 32.0 \, \text{g/mol} = 64000 \, \text{g} = 64 \, \text{kg} \] 3. **
### Problem Statement: A sealed \(86 \, \text{m}^3\) tank is filled with 2000 moles of ideal oxygen gas (diatomic) at an initial temperature of 270 K. The gas is heated to a final temperature of 430 K. The atomic mass of oxygen is \(16.0 \, \text{g/mol}\). The mass density of the oxygen gas, in SI units, is closest to: - \(0.74\) - \(0.56\) - \(0.93\) - \(1.5\) - \(0.37\) ### Answer Choices: - \(0.74\) - \(0.56\) - \(0.93\) - \(1.5\) - \(0.37\) ### Instructions: Click Save and Submit to save and submit. Click Save All Answers to save all answers. --- ### Explanation of Key Concepts: 1. **Ideal Gas Law** - The relationship between pressure (P), volume (V), temperature (T), and number of moles (n) of an ideal gas is given by the equation: \[ PV = nRT \] Where \(R\) is the universal gas constant (\(8.314 \, \text{J/(mol·K)}\)). 2. **Density Calculation** - To find the mass density (\(\rho\)) of the gas, we need to calculate the mass (m) of the gas and then divide it by the volume (V): \[ \rho = \frac{m}{V} \] #### Steps to Calculate Density: 1. **Calculate the Molar Mass**: - The oxygen gas is diatomic, so the molar mass \(M(O_2)\) is \(32.0 \, \text{g/mol}\) (since \(16.0 \, \text{g/mol} \times 2\)). 2. **Calculate the Mass of the Gas**: - Use the number of moles and the molar mass to find the total mass: \[ m = n \times M(O_2) = 2000 \, \text{mol} \times 32.0 \, \text{g/mol} = 64000 \, \text{g} = 64 \, \text{kg} \] 3. **
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![### Problem Statement:
A sealed \(86 \, \text{m}^3\) tank is filled with 2000 moles of ideal oxygen gas (diatomic) at an initial temperature of 270 K. The gas is heated to a final temperature of 430 K. The atomic mass of oxygen is \(16.0 \, \text{g/mol}\). The mass density of the oxygen gas, in SI units, is closest to:
- \(0.74\)
- \(0.56\)
- \(0.93\)
- \(1.5\)
- \(0.37\)
### Answer Choices:
- \(0.74\)
- \(0.56\)
- \(0.93\)
- \(1.5\)
- \(0.37\)
### Instructions:
Click Save and Submit to save and submit. Click Save All Answers to save all answers.
---
### Explanation of Key Concepts:
1. **Ideal Gas Law** - The relationship between pressure (P), volume (V), temperature (T), and number of moles (n) of an ideal gas is given by the equation:
\[
PV = nRT
\]
Where \(R\) is the universal gas constant (\(8.314 \, \text{J/(mol·K)}\)).
2. **Density Calculation** - To find the mass density (\(\rho\)) of the gas, we need to calculate the mass (m) of the gas and then divide it by the volume (V):
\[
\rho = \frac{m}{V}
\]
#### Steps to Calculate Density:
1. **Calculate the Molar Mass**:
- The oxygen gas is diatomic, so the molar mass \(M(O_2)\) is \(32.0 \, \text{g/mol}\) (since \(16.0 \, \text{g/mol} \times 2\)).
2. **Calculate the Mass of the Gas**:
- Use the number of moles and the molar mass to find the total mass:
\[
m = n \times M(O_2) = 2000 \, \text{mol} \times 32.0 \, \text{g/mol} = 64000 \, \text{g} = 64 \, \text{kg}
\]
3. **](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8689a897-6f19-4f8c-bce2-bc1e854b9491%2F036dbb90-37e3-408a-8173-9929a112cd05%2F25rlytr.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
A sealed \(86 \, \text{m}^3\) tank is filled with 2000 moles of ideal oxygen gas (diatomic) at an initial temperature of 270 K. The gas is heated to a final temperature of 430 K. The atomic mass of oxygen is \(16.0 \, \text{g/mol}\). The mass density of the oxygen gas, in SI units, is closest to:
- \(0.74\)
- \(0.56\)
- \(0.93\)
- \(1.5\)
- \(0.37\)
### Answer Choices:
- \(0.74\)
- \(0.56\)
- \(0.93\)
- \(1.5\)
- \(0.37\)
### Instructions:
Click Save and Submit to save and submit. Click Save All Answers to save all answers.
---
### Explanation of Key Concepts:
1. **Ideal Gas Law** - The relationship between pressure (P), volume (V), temperature (T), and number of moles (n) of an ideal gas is given by the equation:
\[
PV = nRT
\]
Where \(R\) is the universal gas constant (\(8.314 \, \text{J/(mol·K)}\)).
2. **Density Calculation** - To find the mass density (\(\rho\)) of the gas, we need to calculate the mass (m) of the gas and then divide it by the volume (V):
\[
\rho = \frac{m}{V}
\]
#### Steps to Calculate Density:
1. **Calculate the Molar Mass**:
- The oxygen gas is diatomic, so the molar mass \(M(O_2)\) is \(32.0 \, \text{g/mol}\) (since \(16.0 \, \text{g/mol} \times 2\)).
2. **Calculate the Mass of the Gas**:
- Use the number of moles and the molar mass to find the total mass:
\[
m = n \times M(O_2) = 2000 \, \text{mol} \times 32.0 \, \text{g/mol} = 64000 \, \text{g} = 64 \, \text{kg}
\]
3. **
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